Question

A piece of cloth cost rupees 200.if the piece was 5m longer and each metre of cloth cost rupees 2 less, the cost of the piece would have remained uncharged. How long is the piece and what is the original rate per metre?

Answer 1

Let the original length of the cloth be x.

Let the rate per metre be y.

A.T.Q


$xy = 200 \: \: \: \: \: ..1 \\ \\ (x + 5)(y - 2) = 200 \\ or \: xy - 2x + 5y - 10 = 200 \\ or \: 200 - 2x + 5y - 10 = 200 \\ (xy = 200) \\ or \: - 2x + 5y - 10 = 0 \\ \\ or \: \frac{ - 2 \times 200}{y} + 5y - 10 = 0 \\ or \: \frac{ - 400 + 5 {y}^{2} - 10y }{y} = 0 \\ or \: - 400 + 5 {y}^{2} - 10y = 0 \\ or \: 5 {y}^{2} - 10y - 400 = 0 \\ or \: {y}^{2} - 2y - 80 = 0 \\ or \: {y}^{2} + 8y - 10y - 80 = 0 \\ or \: y(y + 8) - 10(y + 8) = 0 \\ or \: (y - 10)(y + 8) = 0$

hence y = 10, -8
Since y can't be negative y = 10

$xy = 200 \\ or \: x \times 10 = 200 \\ or \: x = 20$
Answer - Length of cloth is 20m and the rate per metre is ₹10.